The slope of the line that passes through (1, 1) and (7, 5) is 2/3
How to calculate the slope of the line?From the question, the points are given as
a. (1, 1) and (7,5)
Rewrite the above points properly
So, we have the following ordered pairs
(1, 1) and (7,5)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 1) and (7,5)
Substitute the known values in the above equation
So, we have the following equation
Slope = (5 - 1)/(7 - 1)
Evaluate
Slope = 2/3
Hence, the slope of the line is 2/3
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Possible question
Find the slope of the line that passes through a. (1, 1) and (7,5)
My science class is pretty small. There are just 18 students in the class. My
teacher, Ms. Microbe, has an unusual system for pairing us up for labs. She
has given each of us a number from 1 through 18, and on lab days, she pulls
our numbers out of a bag to determine who is paired with whom. When we
did our last lab, I happened to notice that the sum of each person's number
with his/her lab, partner's number was a perfect square!
How were the partners assigned?
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9).
Square numbers:A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.
For example:
Square of 2 = 4
Square of 3 = 9
Square of 4 = 16
Here we have
A science class is pretty small
There are just 18 students in the class.
The teacher gave each of them numbers from 1 through 18 on lab days
Start from 1 and find by adding which number we will get a square number
Here 1 + 15 = 16
2 + 14 = 16
3 + 13 = 16
4 + 12 = 16
5 + 11 = 16
6 + 10 =16
After the above combinations, the remaining numbers are
7, 8, 9, 16, 17, 18
which can be added as given below to get square number 25
=> 18+7=25
=> 17+8=25
=> 16+9=25
Therefore,
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9)
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Ms. Galindo’s class has adopted two equal sections of a highway to keep clean. The combined length of the two sections is
6/8
of a mile. How long is each section?
Each section of a highway has length of 1.5 miles.
In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.
We need to find the length of each section.
Let each section measures x mile.
The combined length of the two sections is 6/8 of a mile.
So, we get an equation x + x = 6/8
We solve above equation to find the value of x.
2x = 6/8
x = (6/8) / 2
x = 6/4
x = 1.5
Therefore, each section of a highway has length of 1.5 miles.
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Will give brainliest. Please it needs to be correct. Refer to the image
Answer: D
PLEASE GIVE BRAINLIEST THANK YOU!!!
Explain how to find the distance between -2 and 3
on a number line.
The distance between -2 and 3 on a number line is 5 units.
What is a number line?
A horizontal line with evenly spaced numerical increments is referred to as a number line. The number on the line depends on how the number is contained.
The Distance Between Two Points on a number line.
The secret to finding the distance between two points is to remember that the geometric definition of subtraction is the distance between the two integers if we subtract the smaller number from the larger one.
Here, we have
the distance between -2 and 0 is 2 units
the distance between 0 and 3 is 3 units
2+3 = 5
OR
3- (-2) =
3+2 = 5
5 units
Hence, the distance between -2 and 3 on a number line is 5 units.
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Number of factors of 10 in 10²
Answer:
24
Step-by-step explanation:
give me brainliest pls
The area of a rectangle is given as 90 cm² and the length is 3 cm longer than its width. Find the length and the width of the rectangle.
Answer:
Step-by-step explanation:
Area of a rectangle is given by the formula :
A = L × W
Substituting 90 with A , x with W and (x+3) with L, we get :
90 = (x+3)×x
Simplifying the right side by expanding the bracket :
x(x+3) =
x²+3x
90=x²+3x
Now we can make a quadratic by subtracting both sides by 90 :
x²+3x-90 =0
I'm not sure about the rest
Use the diagram and the given angle measure to find the other three measures
The other three measures are:
∠1 = 159°∠2 = 21°∠4 = 21°What is Angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.This, I assume, refers to two lines that cross and create four angles.
The sum of the additional angles 2 and 3 is 180°.Angles 2 and 3 equal 180°.159⁰ + angle 2 = 180⁰angle 2 = 180⁰ - 159⁰angle 2 = 21⁰The same applies to angles 2 and 4 since angles 1 and 3 are vertical angles.
Since vertical angles are congruent in measure, it is simple to determine their measurements.
Hence, the three measures are:
∠1 = 159°∠2 = 21°∠4 = 21°To learn more about Angles click on the link
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Ada lives 12 4/5 miles from her aunt's house. she lives 17 3/8 miles from her grandmother's house. how many more miles does jada live from her grandmother's house than her aunt's house?
Answer:
[tex]4 \frac{23}{40}\; \rm miles[/tex]
Step-by-step explanation:
To find how many more miles Ada lives from her grandmother's house than her aunt's house, we need to subtract the distance to her aunt's house from the distance to her grandmother's house.
Ada lives 17 3/8 miles from her grandmother's house.
Ada lives 12 4/5 miles from her aunt's house.
Convert both mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]17 \frac{3}{8}=\dfrac{17 \cdot 8+3}{8}=\dfrac{139}{8}[/tex]
[tex]12 \frac{4}{5}=\dfrac{12 \cdot 5+4}{5}=\dfrac{64}{5}[/tex]
As both improper fractions have a different denominator, we need to change both fractions into equivalent fractions with the same denominator. To do this, find the least common multiple (LCM) of the denominators, 8 and 5.
The LCM of 8 and 5 is 40. Therefore, convert the fractions into their equivalent fractions (with 40 as their denominator) by multiplying the numerator and denominator by the same number:
[tex]\dfrac{139}{8}=\dfrac{139 \cdot 5}{8 \cdot 5}=\dfrac{695}{40}[/tex]
[tex]\dfrac{64}{5}=\dfrac{64 \cdot 8}{5 \cdot 8}=\dfrac{512}{40}[/tex]
Now the fractions have the same denominator, we can carry out the subtraction by simply subtracting the numerators:
[tex]\dfrac{695}{40}-\dfrac{512}{40}=\dfrac{695-512}{40}=\dfrac{183}{40}[/tex]
Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:
[tex]183 \div 40=4\;\rm remainder \;23[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]4 \frac{23}{40}[/tex]
Therefore, Ada lives 4 23/40 miles more from her grandmother's house than her aunt's house.
A construction crew needs to pave a road that is 209 miles long. The crew paves 8 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by the following function.
L(d)=209-8d
Question a.)
If 154 miles of the road is left to be paved, how many days has the crew been paving the road?
Question b.)
How many miles of the road does the crew have left to pave after 13 days?
Answer:
a) 6 7/8 days
b) 105 miles
Step-by-step explanation:
Given that L(d) = 209 -8d miles of road remain to be paved after d days, you want to know (a) the number of days paving if 154 miles remain, and (b) remaining miles after 13 days.
a) Paving daysWe want to find d such that L(d) = 154.
L(d) = 154
209 -8d = 154 . . . . . . substitute for L(d)
209 -154 = 8d . . . . . add 8d-154
55/8 = d = 6 7/8 . . . divide by 8
The crew has been paving for 6 7/8 days if 154 miles remain.
b) Remaining milesAfter 13 days, the remaining miles will be ...
L(13) = 209 -8·13 = 209 -104
L(13) = 105
After 13 days, the crew has 105 miles left to pave.
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Given f(x) = -x - 1, find f(1).
Answer:
f(1) = -2
Step-by-step explanation:
f(1) = -(1) - 1
f(1) = -1 - 1
f(1) = -2
Suzette ran and biked for a total of 50 mi in 4 h. Her average running speed was 5mph and her average biking speed was 15 mph.
Let x= total hours ran
Let y= total hours biked
How many hours did suzette run?
How many hours did she bike?
In total 4 hours Suzette ran for 1 hour and biked for 3 hours having average speed 5mph and 15mph respectively.
What is Average Speed?
Average speed is defined as total distance covered by the body divided by the time taken.
Average speed = Total distance covered/ total time taken
According to the given question:
Let x = total hours ran and y = total hours biked
Total time she ran and biked = 4h
∴ x + y = 4 ----- 1)
Total distance she biked and ran = 50 miles
Now, average running speed = 5 mph
Distance she ran = 5x
Similarly average biking speed = 15 mph
Distance she biked = 15y
∴ 5x + 15y = 50 ----- 2)
Solving 1) and 2) to get the values of x and y
Substituting x = 4 - y from 1) in 2)
5 (4 - y) + 15y = 50
On solving further we get y = 3
Substituting y = 3 to get x
x = 4 - 3
x = 1
Hence the Suzette ran for 1h and biked for 3h.
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The table represents points on a line. What is the slope
X 1 4 7 10
Y 8 6 4 2
Answer:
slope = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 8) and (x₂, y₂ ) = (10, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-8}{10-1}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]
the cat and rabbit's weight is 10 kg and so the dog and rabbit is 20 kg and the dog and cats weight isn24 kg so the question is what their weight togetheer> cat,dog,rabbit??
Answer:
27
Step-by-step explanation:
The cat weighs 7 kg.
The rabbit weighs 3 kg.
The dog weighs 17 kg.
You can check these answers by adding them together.
A cat plus the rabbit is 10 kg.
The rabbit and the dog is 20 kg.
The dog and cat is 24 kg.
when the 171st even positive integer is subtracted from the 219th odd positive integer, the result is z. Find z.
there are 46 students going on a field trip to the museum. if 7 students can fit in each van , how many vans are needed for all 46 students to go to the museum
Answer:
Step-by-step explanation:
NOSEEEEEE
22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
What I
The train takes 6 hours to travel the same distance.
From the question, we have
A train with 20km per hour takes 3 hours to travel the distance .
Another train with 10km per hour takes = (3*20)/10 hours
=6 hours
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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If you rotate point A(-3,4) 180 degrees clockwise and then rotate it again 90 degrees counter clockwise what would be the coordinates of A"?
(3,-4)
(4,3)
(-4,-3)
(-3,-4)
The coordinates of A'', applying the two rotations, are given as follows:
A'' (4, 3).
What is a rotation?A rotation is one example of transformation that a function can undergo, in which the congruence and similarity of the images are kept but the orientation of the image changes.
The rules for each possible rotation are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates are given as follows:
A(-3,4).
After the first 180º clockwise rotation, the coordinates are:
A'(3,-4).
(signals exchanged)
After the final rotation, the 90º counterclockwise rotation, the coordinates of A'' are given as follows:
A'' (4, 3).
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Amir want to proportionally increae the ize of a photo to create a poter for hi room. The ize of the original photo i hown. Complete the tatement and then anwer the quetion to repreent way that Amir can increae the ize of hi photo
The height of the poster is 20 inches.
The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.
The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".
30 = k*6
k = 30/6
k = 5
Hence, the poster is scaled up by a factor of five.
H = k*4
H = 5*4
H = 20
Hence, the height of the scaled-up poster is 20 inches.
The complete question is given below.
Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?
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what type of statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population from which the sample sia sssumed to have been selecteed
We use Inferential Statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population.
Given that;
What kind of statistics is used to gauge the likelihood that a statistical finding based on information from a random sample is representative of the population the sample is presumed to have been drawn from?
Inferential Statistics:
You attempt to conclude using inferential statistics that go beyond the immediate facts alone. For instance, we use inferential statistics to try to infer what the population would think from the sample data. Alternately, we utilize inferential statistics to assess the likelihood that an observed difference between groups in this study is a reliable one or one that may have occurred by chance. Descriptive statistics are used to simply describe what's happening in our data, while inferential statistics are used to conclude more general conditions from our data.
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11. √1156
12. √1024
13. √1225
14. √1764
15. √1936
please ahh little help please
The evaluation of the square roots of the numbers using prime factorization gives;
11. √1156 = 32
12. √1024 = 32
13. √1225 = 35
14. √1764 = 42
15. √1936 = 44
What are prime factors?Prime factors are the factors of a number that are also prime numbers.
The square roots of the numbers found using prime factorization are as follows;
11. √1156
1156 ÷ 2 = 578
578 ÷ 2 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
√1156 = √(2 × 2 × 17 × 17) = √(2² × 17²)
√1156 = √(2² × 17²) = 2 × 17 = 34
√1156 = 34
12. √1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
Therefore; √(1024) = √(2×2×2×2 ×2×2×2×2×2×2) = √(2¹⁰) = 2⁵ = 32
√1024 = 32
13. √1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Therefore;
√(1225) = √(5 × 5 × 7 × 7) = √(5² + 7²) = 5 × 7 = 35
14. √1764
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
√1764 = √(2 × 2 × 3 × 3 × 7 × 7) = √(2² × 3² × 7² = 2 × 3 × 7 = 42
15. √1936
1936 ÷ 2 = 968
968 ÷ 2 = 484
484 ÷ 2 = 242
242 ÷ 2 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
Therefore; √(1936) = √(2 × 2 × 2 × 2 × 11 × 11) = √(2⁴ × 11²) = 2² × 11
√(1936) = 2² × 11 = 44
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What are the first 5 terms
The first five terms of the given sequence are a₁ = 50, a₂ = 25, a₃ = 12.5, a₄ = 6.25 and a₅ = 3.125.
What is a geometric sequence?In a geometric sequence the ratio of any two consecutive terms are equal. This ratio is known as the common ratio of the sequence.
Given that,
a₁ = 50 and aₙ = aₙ₋₁ ÷ 2
The first five terms are a₁, a₂, a₃, a₄ and a₅.
All the terms can be written using aₙ = aₙ₋₁ ÷ 2 as follows,
a₂ = a₁ ÷ 2
⇒ a₂ = 50 ÷ 2
⇒ a₂ = 25
a₃ = a₂ ÷ 2
⇒ a₃ = 25 ÷ 2
⇒ a₃ = 12.5
a₄ = a₃ ÷ 2
⇒ a₄ = 12.5 ÷ 2
⇒ a₄ = 6.25
a₅ = a₄ ÷ 2
⇒ a₅ = 6.25 ÷ 2
⇒ a₅ = 3.125
Hence, the first five terms are 50, 25, 12.5, 6.25 and 3.125 respectively.
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reduce with all steps
A fast food restaurant was selling 2 boxes of chicken nuggets for $4.52
A competing restaurant was selling 4 boxes of chicken fingers for $9.44
Which food has a higher unit price?
Answer: The competing restaurant
Step-by-step explanation:
If you divide the 4.52 by 2 you get 2.26 for the first restaurant's unit price
If you divide the 9.44 by 2 you get 2.36 for the second restaurant's unit price
Hope this helps :)
Segment RS is reflected over the line y = and then translated by (x +3, y + 4). The resulting segment
R" S" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
R=
S =
Answer:
-1,-2
Step-by-step explanation:
get the x and y value and combine the coordinates using the slope formula
You have a gift certificate to a book store worth $95. Each paperback books is $10 and each hardcover books is
$17. You must spend at least $20 in order to use the gift certificate. Write and graph a system of inequalities to
model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number
of hardback books
Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,
⇒ what you buy should be ≥ 20
Input the price to the inequality above
⇒ what you buy should be ≥ 20
⇒ paperback price + hardcover price ≥ 20
⇒ 10x + 17y ≥ 20
Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms
⇒ x ≥ 0
⇒ y ≥ 0
So this is the summary
10x + 17y ≥ 20
x ≥ 0
y ≥ 0
Step-by-step explanation:
each day for five days, you collect a sample of 200 buns coming out of a commercial oven. you record the number of burned buns in the table below. the standard deviation (sigma) is 0.025. what is the upper control limit? state your answer to two decimal places, for example 0.12
The upper limit is 0.79
The class interval's upper limit is its highest value. Similarly, the lower limit is the class interval's smallest value.
Given that n = 200 and standard deviation σ = 0.025
σ = (√n/√n) = 0.025
Now calculate p
P = defectives/total inspected
= 145/200
P = 0.72
Q= 1-p
= 1- 0.72
= 0.18
Now calculate the upper limit
UCL = p – (-3 x σ)
= 0.72 – ( -3 x 0.025)
= 0.72 – (-0.075)
= 0.72 + 0.075
= 0.795
= 0.79
Therefore the upper limit is 0.79
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Games at the carnival costs $9 each. The prizes awarded to the winners costs the owner $207.35. How many games must be played for the owner to make more than $100.
Write and solve an inequality. Show your work using 3 or 4 steps. Use g as your variable. Round your initial answer to the nearest hundredth.
The inequality used to represent games at carnival is 9g - 207.35 > 100
The solution is g > 34.15
How to determine the inequality used to represent games at carnivalInformation gotten from the question include
Games at the carnival costs $9 each
The prizes awarded to the winners costs the owner $207.35
How many games must be played for the owner to make more than $100 = ?
Using g as variable which is the number of games to be played we have
total amount gotten from games = 9 * g
prizes of winners = 207.35
The inequality equation as described in the problem is represented using linear function as as follows
9g - 207.35 > 100
for the owner to make more than 100 we have the equation
total amount gotten from games - prizes of winners > 100
9g - 207.35 > 100
100 + 207.35 < 9g
9g > 307.35
g > 34.15
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PLEASE HELP!
3. In a survey of 1000 eligible voters selected at random, it was found that 8% had a college degree. Additionally it was found that 80% of those who had a college degree voted in the last presidential election. Whereas 55% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random voted. Draw a diagram to represent this situation.
a) If you randomly chose an eligible voter from this group, what is that probability that they have a degree and did not vote?
b) If you randomly chose an eligible voter from this group, what is the probability that they voted?
c) If you randomly chose a person who voted in the presidential election, what is the probability that they had a college degree?
hello, i'm sorry but i can't graph the diagram but here are the answers for a-c :)
A. 8%
B. 39.6%
C. 58.4%
step by step:
A. Calculation to determine the probability of The voter had a college degree and voted in the last presidential election.
P = 80/1,000
P=0.08*100
P=8%
Therefore the probability of The voter had a college degree and voted in the last presidential election will be 8%
B. Calculation to determine the probability of The voter did not have a college degree and did not vote in the last presidential election.
P =396/1000
P=0.396*100
P=39.6%
Therefore the probability of The voter did not have a college degree and did not vote in the last presidential election will be 39.6%
C. Calculation to determine the probability if The voter voted in the last presidential election.
P = 584/1,000
P=0.584*100
P=58.4%
Therefore the probability if The voter voted in the last presidential election will be 58.4%
Evaluate -7(x - 4y) when x = -4 and y = -6.
A 140
B 52
C-28
D-140
Answer: D
Step-by-step explanation:
Take the equation and substitute the variables for the numbers given
-7(-4-4(-6))=-140
Hope this helps :)
To compleate a task in 16 days a company needs 5 workers each working 6 hours per day
The company decides to have 8 people each working 4 hours per day
Assuming that each person works at the same rate
How many days will the task take to complete?
Answer:
10 days
Step-by-step explanation:
This is a type of proportion either direct or indirect .16 days for 5 workers.so for 8 workers the days will reduce .Now for 8 workers it will be 10days